Contrasting Behavior of the Z Bonds in X-Z···Y Weak Interactions: Z = Main Group Elements Versus the Transition Metals

Anisotropic Thermal Expansion of Structurally Related Lanthanide-Mercury(II) Cyanide Coordination Polymers

Three sets of related lanthanide-mercury(II) cyanide coordination polymers were synthesized by the reaction of LnCl3·xH2O (Ln = Ce, Nd, Eu, Gd, Tb, Dy, Ho, Tm, Yb, and Lu) with Hg(CN)2 and structurally characterized. [Ce(OH2)5][Hg(CN)2Cl]3·2H2O is a 3-D material with sheet-based architecture; its thermal expansion behavior shows uniaxial negative thermal expansion (-18.3(8), 39(2), and 68.3(16) ppm K-1 along the a, b, and c axes, respectively). This anisotropic thermal behavior is postulated to be driven elastically by weak Hg···Cl interactions: large area expansion of the sheets causes negative thermal expansion in the perpendicular direction. Using lanthanides heavier than Ce yielded 2-D sheet-based compounds with the formula [Ln(OH2)x]2[Hg(CN)2]5Cl6·2H2O (Ln = Nd and Eu, x = 7; Ln = Gd, Tb, Dy, Ho, Tm, Yb, and Lu, x = 6). Although there was also evidence for elastic behavior within these materials, both showed uniaxial zero thermal expansion (Ln = Nd: 27.9(17), 22.4(10), and 0.6(12) ppm K-1 along the I, II, and III principal axes, respectively; Ln = Tb: 39.6(12), 1.1(17), and 36.1(7) ppm K-1 along the a, b, and c axes, respectively). Despite their similar structural architecture, this zero thermal expansion was found to occur in different directions─within the plane of the 2-D sheets for [Nd(OH2)7]2[Hg(CN)2]5Cl6·2H2O but in the direction perpendicular to the 2-D sheets for [Tb(OH2)6]2[Hg(CN)2]5Cl6·2H2O. Overall, this system of compounds reveals the delicate relationship between coordination polymer structure and thermal expansion.

Spodium bonding in bis(alkynyl)mecurials

The new bis(alkynyl)mercurial Hg{CCSeCW(CO)2(Tp*)}2 (Tp* = tris(dimethylpyrazolyl)borate) forms adducts with fluoride and phenathroline, the structures of which are interpreted in the context of two-coordinate mercury presenting a σ-torroid for spodium bonding.

Unified classification of non-covalent bonds formed by main group elements: a bridge to chemical bonding

Using correlation plots of binding energy and electron density at the bond critical point, we investigated the nature of intermolecular non-covalent bonds (D-X⋯A, where D = O/S/F/Cl/Br/H, mostly, X = main group elements (except noble gases), A = H2O, NH3, H2S, PH3, HCHO, C2H4, HCN, CO, CH3OH, and CH3OCH3). The binding energies were calculated at the MP2 level of theory, followed by Atoms in Molecules (AIM) analysis of the ab initio wave functions to obtain the electron density at the bond critical point (BCP). For each non-covalent bond, the slopes of the binding energy versus electron density plot have been determined. Based on their slopes, non-covalent bonds are classified as non-covalent bond closed-shell (NCB-C) or non-covalent bond shared-shell (NCB-S). Intriguingly, extrapolating the slopes of the NCB-C and NCB-S cases leads to intramolecular "ionic" and "covalent" bonding regimes, establishing a link between such intermolecular non-covalent and intramolecular chemical bonds. With this new classification, hydrogen bonds and other non-covalent bonds formed by a main-group atom in a covalent molecule are classified as NCB-S. Atoms found in ionic molecules generally form NCB-C type bonds, with the exception of carbon which also forms NCB-C type bonds. Molecules with a tetravalent carbon do behave like ions in ionic molecules such as NaCl and interact with other molecules through NCB-C type bonds. As with the chemical bonds, there are some non-covalent bonds that are intermediate cases.

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

Insight into Spodium–π Bonding Characteristics of the MX2···π (M = Zn, Cd and Hg; X = Cl, Br and I) Complexes—A Theoretical Study

The spodium–π bonding between MX₂ (M = Zn, Cd, and Hg; X = Cl, Br, and I) acting as a Lewis acid, and C₂H₂/C₂H₄ acting as a Lewis base was studied by ab initio calculations. Two types of structures of cross (T) and parallel (P) forms are obtained. For the T form, the X–M–X axis adopts a cross configuration with the molecular axis of C≡C or C=C, but both of them are parallel in the P form. NCI, AIM, and electron density shifts analyses further, indicating that the spodium–π bonding exists in the binary complexes. Spodium–π bonding exhibits a partially covalent nature characterized with a negative energy density and large interaction energy. With the increase of electronegativity of the substituents on the Lewis acid or its decrease in the Lewis base, the interaction energies increase and vice versa. The spodium–π interaction is dominated by electrostatic interaction in most complexes, whereas dispersion and electrostatic energies are responsible for the stability of the MX₂⋯C₂F₂ complexes. The spodium–π bonding further complements the concept of the spodium bond and provides a wider range of research on the adjustment of the strength of spodium bond.

Yet another perspective on hole interactions

Hole interactions are known by different names depending on the key atom of the bond (halogen bond, chalcogen bond, hydrogen bond, etc.), and the geometry of the interaction (σ if in line, π if perpendicular to the Lewis acid plane). However, its origin starts with the creation of a Lewis acid by an underlying covalent bond, which forms an electrostatic depletion and a virtual antibonding orbital, which can create non-covalent interactions with Lewis bases. In this (maybe subjective) perspective, we will claim that hole interactions must be defined via the molecular orbital origin of the molecule. Under this premise we can better explore the richness of such bonding patterns. For that, we will study old, recent and new systems, trying to pinpoint some misinterpretations that are often associated with them. We will use as exemplars the triel bonds, a couple of metal complexes, a discussion on convergent σ-holes, and many cases of anti-electrostatic hole interactions.

Group 12 Carbonates and their Binary Complexes with Nitrogen Bases and FH2 Z Molecules (Z=P, As, Sb): Synergism in Forming Ternary Complexes

MCO₃ (M=Zn, Cd, Hg) forms a spodium bond with nitrogen-containing bases (HCN, NHCH₂ , NH₃ ) and a pnicogen bond with FH₂ Z (Z=P, As, Sb). The spodium bond is very strong with the interaction energy ranging from -31 kcal/mol to -56 kcal/mol. Both NHCH₂ and NH₃ have an equal electrostatic potential on the N atom, but the corresponding interaction energy is differentiated by 1.5-4 kcal/mol due to the existence of spodium and hydrogen bonds in the complex with NHCH₂ as the electron donor. The spodium bond is weakest in the HCN complex, which is not consistent with the change of the binding distance. The spodium bond becomes stronger in the CdCO₃ <ZnCO₃ <HgCO₃ sequence although the positive electrostatic potential on the Hg atom is smallest. This is because the electrostatic interaction is dominant in the spodium-bonded complexes of CdCO₃ and ZnCO₃ but the polarization interaction in that of HgCO₃ . The pnicogen bond is much weaker than the spodium bond and the former has a larger enhancement than the latter in the FH₂ Z⋅⋅⋅OCO₂ M⋅⋅⋅N-base ternary complexes.

Study of Beryllium, Magnesium, and Spodium Bonds to Carbenes and Carbodiphosphoranes

The aim of this article is to present results of theoretical study on the properties of C⋯M bonds, where C is either a carbene or carbodiphosphorane carbon atom and M is an acidic center of MX2 (M = Be, Mg, Zn). Due to the rarity of theoretical data regarding the C⋯Zn bond (i.e., the zinc bond), the main focus is placed on comparing the characteristics of this interaction with C⋯Be (beryllium bond) and C⋯Mg (magnesium bond). For this purpose, theoretical studies (ωB97X-D/6-311++G(2df,2p)) have been performed for a large group of dimers formed by MX2 (X = H, F, Cl, Br, Me) and either a carbene ((NH2)2C, imidazol-2-ylidene, imidazolidin-2-ylidene, tetrahydropyrymid-2-ylidene, cyclopropenylidene) or carbodiphosphorane ((PH3)2C, (NH3)2C) molecule. The investigated dimers are characterized by a very strong charge transfer effect from either the carbene or carbodiphosphorane molecule to the MX2 one. This may even be over six times as strong as in the water dimer. According to the QTAIM and NCI method, the zinc bond is not very different than the beryllium bond, with both featuring a significant covalent contribution. However, the zinc bond should be definitely stronger if delocalization index is considered.

Assessing the Orbital Contribution in the "Spodium Bond" by Natural Orbital for Chemical Valence-Charge Displacement Analysis

The term "spodium bond" (SpB) has been recently proposed to describe the noncoordinative interaction that can be established between a polarized group 12 metal and a mild Lewis base (LB). Most of the systems showing short metal-donor distances compatible with SpB are characterized by the coexistence of multiple weak interactions, including hydrogen and halogen bonding, making the assessment of real importance of SpB difficult. Here, we show that the relative importance of each contribution can be probed by dissecting the orbital component of the interaction through the extended transition state-natural orbital for chemical valence-charge displacement analysis (ETS-NOCV-CD). The latter gives useful information about relative energies and electrons involved, for model systems ([(thiourea)₂MX₂]···LB; M = Zn, Cd, and Hg; X = Cl and I; and LB = CH₂S, CH₂O, CH₃CN, and CO) and a variety of structures extracted from experimentally characterized adducts, allowing us to demonstrate the lack of a direct correlation between a favorable metal-base distance and the presence of an orbital contribution for the SpB.

Spodium bonding in five coordinated Zn(ii): a new player in crystal engineering?

This highlight evidences the existence and importance of spodium bonds (SpB) in solid state structures involving five-coordinated square-pyramidal Zn(ii) spodium atom.

Differentiating intramolecular spodium bonds from coordination bonds in two polynuclear zinc(ii) Schiff base complexes

Two new zinc(ii) complexes have been synthesized and characterized. Theoretical study is devoted to distinguish between conventional coordination bonds and spodium bonds between the zinc and oxygen centers.

Coordination versus spodium bonds in dinuclear Zn(ii) and Cd(ii) complexes with a dithiophosphate ligand

Two new d10-metal dithiophosphate complexes have been synthesized in purely aqueous media and characterized by elemental and spectral analyses. DFT calculations, QTAIM and NCI Plot index methods are preformed to differentiate the coordination and spodium bonds in the complexes.

Intramolecular Spodium Bonds in Zn(II) Complexes: Insights from Theory and Experiment

Two new dinuclear zinc(II) complexes, [Zn₂(µ_1,3-OAc)(L¹)₂]I·MeOH (1) and [Zn₂(µ_1,3-OAc)(L²)(NCS)] (2), (where HL¹ = 2-(((3-(dimethylamino)propyl)amino)methyl)-6-methoxy-phenol and H₂L² = 2,2′-[(1-Methyl-1,2-ethanediyl)bis(iminomethylene)]bis[6-ethoxyphenol]) have been synthesized and characterized by elemental and spectral analysis. Their X-ray solid state structures have been determined, revealing the existence of intramolecular Zn···O spodium bonds in both complexes due to the presence of methoxy (1) or ethoxy (2) substituents adjacent to the coordinated phenolic O-atom. These noncovalent interactions have been studied using density functional theory (DFT) calculations, the quantum theory of “atoms-in-molecules” and the noncovalent interaction plot. Moreover, a search in the Cambridge structure database (CSD) has been conducted in order to investigate the prevalence of intramolecular spodium bonds in Zn complexes. To our knowledge this is the first investigation dealing with intramolecular spodium bonds.

Spodium Bonds: Noncovalent Interactions Involving Group 12 Elements

The term spodium (Sp) bond is proposed to refer to a net attractive interaction between any element of Group 12 and electron-rich atoms (Lewis bases or anions). These noncovalent interactions are markedly different from coordination bonds (antibonding Sp-ligand orbital involved). Evidence is provided for the existence of this interaction by calculations at the RI-MP2/aug-cc-pVTZ level of theory, atoms-in-molecules, and natural bond orbital analyses and by examining solid-state structures in the Cambridge Structure Database.

Covalent vs Charge-Shift Nature of the Metal-Metal Bond in Transition Metal Complexes: A Unified Understanding

We present here a general conceptualization of the nature of metal-metal (M-M) bonding in transition-metal (TM) complexes across the periods of TM elements, by use of ab initio valence-bond theory. The calculations reveal a dual-trend: For M-M bonds in groups 7 and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving down to the 5d-series, the bonds become gradually covalent. In contrast, M-M bonds of metals having filled d-orbitals (groups 11 and 12) behave oppositely; initially the M-M bond is covalent, but upon moving down the Periodic Table, the CSB character increases. These trends originate in the radial-distribution-functions of the atomic orbitals, which determine the compactness of the valence-orbitals vis-à-vis the filled semicore orbitals. Key factors that gauge this compactness are the presence/absence of a radial-node in the valence-orbital and relativistic contraction/expansion of the valence/semicore orbitals. Whenever these orbital-types are spatially coincident, the covalent bond-pairing is weakened by Pauli-repulsion with the semicore electrons, and CSB takes over. Thus, for groups 3-10, which possess (n - 1)s²(n - 1)p⁶ semicores, this spatial-coincidence is maximal at the 3d-transition-metals which consequently form charge-shift M-M bonds. However, in groups 11 and 12, the relativistic effects maximize spatial-coincidence in the third series, wherein the 5d¹⁰ core approaches the valence 6s orbital, and the respective Pauli repulsion generates M-M bonds with CSB character. These considerations create a generalized paradigm for M-M bonding in the transition-elements periods, and Pauli repulsion emerges as the factor that unifies CSB over the periods of main-group and transition elements.

Not Only Hydrogen Bonds: Other Noncovalent Interactions

In this review, we provide a consistent description of noncovalent interactions, covering most groups of the Periodic Table. Different types of bonds are discussed using their trivial names. Moreover, the new name “Spodium bonds” is proposed for group 12 since noncovalent interactions involving this group of elements as electron acceptors have not yet been named. Excluding hydrogen bonds, the following noncovalent interactions will be discussed: alkali, alkaline earth, regium, spodium, triel, tetrel, pnictogen, chalcogen, halogen, and aerogen, which almost covers the Periodic Table entirely. Other interactions, such as orthogonal interactions and π-π stacking, will also be considered. Research and applications of σ-hole and π-hole interactions involving the p-block element is growing exponentially. The important applications include supramolecular chemistry, crystal engineering, catalysis, enzymatic chemistry molecular machines, membrane ion transport, etc. Despite the fact that this review is not intended to be comprehensive, a number of representative works for each type of interaction is provided. The possibility of modeling the dissociation energies of the complexes using different models (HSAB, ECW, Alkorta-Legon) was analyzed. Finally, the extension of Cahn-Ingold-Prelog priority rules to noncovalent is proposed.

Regium bonds between Mn clusters (M = Cu, Ag, Au and n = 2-6) and nucleophiles NH3 and HCN

The most stable geometries of the coinage metal (or regium) atom (Cu, Ag, Au) clusters Mn for n up to 6 are all planar, and adopt the lowest possible spin multiplicity. Clusters with even numbers of M atoms are thus singlets, while those with odd n are open-shell doublets. Examination of the molecular electrostatic potential (MEP) of each cluster provides strong indications of the most likely site of attack by an approaching nucleophile, generally one of two positions. A nucleophile (NH3 or HCN) most favorably approaches one particular M atom of each cluster, rather than a bond midpoint or face. In the closed-shell clusters, the interaction energies are highly dependent upon the intensity of the MEP, but this correlation fades for the open-shell systems studied in this work. The strength of the interaction is also closely related to the basicity of the nucleophile. Regium bond energies can be more than 30 kcal mol-1 and tend to follow the Au > Cu > Ag order. These interaction energies are in large part derived from Coulombic attraction, with a smaller orbital interaction contribution.

Regium-π bonds: An Unexplored Link between Noble Metal Nanoparticles and Aromatic Surfaces

The ability of metal clusters involving elements from group 11 (Ag, Cu, Au) to favorably interact with π systems of different size and electronic nature was evaluated at the PBE0-D3/def2-TZVPP//PBE0-D3/def2-TZVP level of theory. The M₉ clusters (M=Cu, Ag, Au) were used as σ-hole and σ-lump donors, and benzene, trifluorobenzene, and hexafluorobenzene as aromatic rings. In addition, the study was expanded to the analysis of extended π systems by using naphthalene and anthracene as well as their corresponding perfluorinated derivatives. Furthermore, Bader's theory of Atoms in Molecules as well as natural bonding orbital and spin-density calculations were used to further investigate and characterize the regium-π and σ-lump complexes described herein. Apparently, regium-π bonds have not previously been described in the literature and may be of great importance in the understanding of organocatalytic processes involving aromatic substrates as well as in the design of new materials based on this novel subclass of σ-hole bonding.

Hydrogen bonds, and σ-hole and π-hole bonds – mechanisms protecting doublet and octet electron structures

For various interactions electron charge shifts try to protect the former doublet or octet electronic structure of the Lewis acid centre.

A halogen bond route to shorten the ultrashort sextuple bonds in Cr2 and Mo2

Selective extraction of destabilizing σ-electrons from the sextuple bond of Cr₂ and Mo₂via σ-hole on a halogen bond donor shortens and strengthens the ultra-short metal–metal bond.